As I did last semester, I had my students (all elementary education majors) do mini-research projects and present at a small poster session.
As before, these posters were optional, although a student cannot get an A for the semester without doing one. I have 37 students, and 24 choose to do a poster. Unlike last semester, there was no paper that accompanied the poster.
Also unlike last semester, I did not hold the poster session during class time. Instead, I integrated it into the campus-wide “Scholarship and Creativity Day.” There were no classes this day—it is a day completely devoted to showing off students’ creative projects.
Here were my suggested projects:
- Note that and do not have repeating decimals; we say that they “terminate.” How can you tell which fractions in Martian arithmetic will terminate?
- Consider extensions of our Last Cookie game (basically, a Nim game). What is you could remove either 2 or 3 cookies per round, but not 1? What if you could do 1,2, or 4 What about other combinations?
- There is a division algorithm called “Egyptian division.” Explain (as we have been doing) why this gives the correct answer to a division problem.
- Learn about “casting out nines,” a method that helps you determine if you did an arithmetic question correctly. Explain why this method works.
- There is a fast and easy way to determine if a number is divisible by 3 in base ten. Explain why this method works.
- There is are not-so-fast and not-so-easy ways to determine if a number is divisible by 7 in base ten. Explain why one of these methods work.
- Explain divisibilty results for other bases (can you easily tell when a number is even/divisible by 3/5/7/etc in base six? Base eight?)
- Research one algorithm from the Trachtenberg System, and explain why it is guaranteed to give the correct answer.
- Teach Mayan students how to use our number system.
- Come up with your own topic (talk to me about it first).
By far, most students choose the “divisibility by 3” or “casting out nines” problems, a reasonable amount choose “teach Mayan students about base ten” “the Last Cookie” problem. Three others did a Trachtenberg problem, one student chose to explain “Egyptian Division,” and two explained why a finger trick works for multiplication by nine.
Many of the presentations were excellent, and many still had trouble understanding what the question is. This was expected. What was not expected was the number of students who participated: I expected about half the number I had.
Finally, many professors from other departments approached me to compliment the poster session. In fact, the dean of the college referenced one of my students’ posters in an address later that evening.
I must remember to try to do this again in most of my classes.